The current US Social Security system provides retirees with a real annuity during their

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3 It is better to have a permanent income than to be fascinating. - Oscar Wilde, The Model Millionaire: A Note of Admiration The current US Social Security system provides retirees with a real annuity during their retirement years. After a worker s Primary Insurance Amount has been determined at the point of retirement, the purchasing power of Social Security benefits remains fixed for the balance of the individual s life. This is accomplished by indexing retirement benefits to annual changes in the Consumer Price Index (CPI). Hence retirees are insulated from inflation risk, at least as long as their consumption bundle is not dissimilar to the bundle used to compute the CPI. Several current reform plans propose to supplement, or partially replace, the existing definedbenefit Social Security system with mandatory individual defined contribution accounts (cf. Gramlich, 1996; Mitchell, Myers and Young, 1999; NASI, 1998). In most individual account plans, retirees would be required to purchase an annuity with all or part of their accumulated account balances. Yet the existing market for individual annuities in the United States is small, the expected present value of annuity payouts is typically below the purchase price of the annuity, and virtually all annuities currently available offer nominal rather than real payout streams. This has led some to argue that individual account plans would expose retirees to inflation risk that they do not currently face, in that they might purchase nominal annuities with their accumulated funds. In this paper, we explore four issues concerning real annuities, nominal annuities, and the inflation risks faced by prospective retirees, all of which are relevant to the prospects for individual accounts under Social Security reform. We begin by describing the annuity market in the United Kingdom. Annuitants in the U.K. can select from a wide range of both real and nominal annuity products. The U.K. annuity market demonstrates the feasibility of offering real annuities in the private marketplace. Moreover, the current U.K. annuity market may indicate the direction in which the U.S. annuity market will evolve, since indexed bonds promising a fixed real return to investors have been available in Britain for nearly two decades. The availability of such bonds has made it possible for U.K. insurers to offer real annuity products without bearing inflation risk. Similar bonds have been available

4 in the United States for only two years. Our evaluation of the U.K. annuity market includes an analysis of the relative prices of both real and nominal annuities, and we present estimates of how much a potential annuitant must pay to purchase the inflation insurance provided by a real annuity. Next we turn to the annuity market in the United States and investigate the availability of real annuities in this country. In early 1997 the U.S. government introduced Treasury Inflation Protection Securities (TIPS) and since then, two products that might be described as inflation indexed annuities have come to market. One, offered by Irish Life Company of North America (ILONA), promises a constant purchasing power stream of benefits. Though this product offers buyers a real stream of annuity payouts, to date it has not been a commercial success. The second, offered by TIAA-CREF, is a variable payout annuity with payouts linked to returns on the CREF Index-Linked Bond Account. We describe the operation of the latter account in some detail, and explain why in practice the TIAA-CREF variable annuity proves not be an inflation-indexed annuity. Hence our analysis of these two products leads us to conclude that there are no commercially significant real annuities available in the U.S. annuity market at the present time. We then go on to consider whether a retiree could use a portfolio of stocks or bonds to hedge long-term inflation risk, in lieu of a portfolio of indexed bonds. Specifically, we evaluate how much inflation risk annuitants would bear if, instead of purchasing nominal annuities, they purchased variable payout annuities with payouts linked to various asset portfolios. The potential inflation protection provided by alternative variable payout annuities is assessed using historical correlation patterns between inflation and nominal returns on stocks, bonds, and bills. The final portion of the analysis explores the expected utility consequences of annuitizing retirement resources in alternative ways. A stylized model is used to calculate the expected lifetime utility of a retiree who could purchase a nominal annuity (thereby bearing inflation risk), a real annuity, and a variable-payout equity-linked annuity. We calibrate this model using available estimates of risk aversion, mortality risks, and the stochastic structure of real returns on corporate stocks. Our results suggest that for plausible values of risk aversion, retirees would not pay very much for the opportunity to 2

5 purchase a real rather than a nominal annuity. This finding is sensitive, however, to assumptions regarding the stochastic process for inflation. Very high expected inflation rates, or very high levels of inflation variability, can lead to a different conclusion. We also find that a variable payout annuity, with payouts linked to the returns on a portfolio of common stocks, is more attractive than a real annuity for consumers with modest risk aversion. This result rests on assumptions about the expected return on stocks relative to riskless assets and hence must be viewed with some caution, since there is substantial prospective uncertainty about expected stock returns. The finding nevertheless illustrates the potentially important role of variable payout annuities as devices for annuitizing assets from individual accounts. The paper is divided into five sections. Section one presents findings on the real and nominal annuity markets in the United Kingdom; the next section describes two inflation linked annuities offered in the United States. Section three reports findings on the correlation between unexpected inflation and real returns on various financial assets and summarizes previous research on this relationship. This section also presents evidence on the ex post real payout streams that would have been paid to retirees had they purchased variable payout annuities at different dates over the last seventy years. The fourth section outlines our algorithm for evaluating the utility benefits of access to various types of annuity products. We report on the wealth equivalent of different annuitization options and link this work with the rapidly growing literature on lifetime portfolio allocation in the presence of financial market and inflation risk. In a brief concluding section we sketch directions for future work. 1. The Market for Real Annuities in the United Kingdom We begin our analysis by describing the real annuity market in the United Kingdom, since these annuities provide important evidence on both the feasibility of providing real annuities through private insurers as well as the consumer costs of buying inflation insurance. We then calculate the expected present discounted value of payouts on real and nominal annuities currently available in the U.K. 3

6 1.1 The Current Structure of the U.K. Annuity Market Annuities providing a constant real payout stream are widely available in the United Kingdom. This is partly due to the fact that government-issued indexed bonds have been available in the U.K. for nearly two decades. Insurance companies holding these bonds can hedge the price level risk that is associated with offering annuity payouts denominated in real rather than in nominal terms. Blake (1999) reports that insurers offering nominal annuities typically back them by holding nominal government bonds, while those offering real annuities hold indexed bonds. The two segments of the individual annuity market in the United Kingdom are defined according to where funds used to purchase the annuity are accumulated. One market segment involves annuities purchased with tax-qualified retirement funds, while the other segment is focused on annuities purchased outside such plans. Qualified retirement plans in Britain include defined benefit occupational pension schemes and personal pension plans (PPPs). Most occupational plans are defined benefit plans, and the annuities that are paid out to their beneficiaries are not purchased in the individual annuity market. PPPs, available since 1988, are retirement saving plans that are broadly similar to Individual Retirement Accounts in the United States. (Prior to 1988, a similar type of plan was available to self-employed individuals.) Contributions to PPPs are tax-deductible, and income on the assets held in such plans is not taxed until the funds are withdrawn. Budd and Campbell (1998) report that in the early 1990s, roughly one quarter of U.K. workers participated in a personal pension plan. Personal pension plans are likely to account for most of the purchases of qualified annuities, since defined contribution plans constitute a minority of U.K. occupational pensions. Those who reach retirement age with assets in a defined contribution occupational pension, or with assets in a personal pension plan, are legally required to annuitize at least part of their pension accumulations. For this reason, the U.K. market for annuities purchased with funds from qualified pension plans is known as the compulsory annuity market. In recent years there has been some relaxation of the rules requiring annuitization. Currently, a retiree can withdraw up to one quarter of a 4

7 personal pension plan accumulation as a lump sum distribution, and assets can be held in the PPP up to age 75 before they must be annuitized. The U.K. annuity arena is also characterized by a second group of voluntarily purchased annuities, known as the "noncompulsory market. In this second market segment, funds accumulated outside of qualified retirement plans are used to purchase annuity products. As other analysts of the individual annuity market have emphasized, demographic characteristics and mortality prospects of annuity buyers in the compulsory and non-compulsory markets are likely to differ. The set of people that purchases annuities in a voluntary purchase market is likely to have better mortality prospects (i.e. a longer life expectancy) as compared to randomly selected individuals in the population. For this reason, workers with PPPs or covered by defined contribution occupational plans are probably not a random subset of the population; their longevity prospects are likely to be better than those of the population at large. Finkelstein and Poterba (1999) compare the U.K. compulsory and noncompulsory annuity markets and show that payouts as a fraction of premiums are somewhat lower in the non-compulsory market. But the extent of adverse selection among annuitants receiving employer pensions is anticipated to be smaller than among people buying individual annuities outside a retirement plan. Our analysis focuses on annuities offered in the compulsory annuity marketplace. The compulsory annuitization requirement for Personal Pension Plans has created a substantial group of retirement-age individuals in the U.K. who must purchase an annuity. To service their needs, annuity brokers exist to help retirees obtain quotes on annuity products. We contacted several of these brokers for data on UK annuity prices and the terms of annuity contracts. Though we have not established precisely how much of the annuity market our sample firms cover, it does appear that we have identified most of the major annuity providers. To focus the discussion we restrict our attention to nominal and inflation-linked single life annuity products. Here the term nominal is used to refer to values denominated in current pounds (or dollars), while real refers to inflation-corrected pounds or dollars. The analysis was conducted using nine insurance companies offering Retail Price Index (RPI)-linked single life annuity policies, and fourteen 5

8 companies offering nominal single-life products. (By comparison, there are nearly one hundred insurance companies offering individual annuity products in the United States, according to A.M. Best s surveys.) We do not consider graded nominal annuity policies that offer a rising stream of nominal benefits over the life of the annuitant at a pre-specified nominal escalation rate. Graded annuities provide annuitants with a way of backloading the real value of payouts from their annuities, but they do not insure against inflation fluctuations as real annuities do. We focus our attention on policies that were available in late August, 1998, and we consider annuities with a 100,000 purchase price (premium). Table 1 reports mean monthly payouts for both nominal and RPI-linked annuities for the firms in our sample. The first two columns show the sample average payout for each type of annuity. They indicate that the first-month payout on a real annuity is between 25 and 30 percent lower than the firstmonth payout on a nominal annuity. This reduction in initial benefits is sometimes cited as the reason some consumers shy away from indexed annuities. The data also indicate differences in the ratio of nominal to real annuity payouts across age groups (real annuities are priced more favorably with rising age), and between men and women (real annuities are priced more favorably for men). These presumably reflect mortality-related differences in the expected duration of payouts under different annuity contracts. We also see substantial variation in the annuity benefits paid by the different insurers, as was previously found for the U.S. annuity market (Mitchell, Poterba, Warshawsky, and Brown, hereafter MPWB; 1999). The third and fourth columns of Table 1 report the coefficient of variation for monthly annuity payouts in both markets; here we see that the pricing of indexed annuities varies more than that of nominal annuities. For five of the six products defined by age and gender of buyer, the coefficient of variation is greater for the real than for the nominal annuity. This may be due to the fact that the effective duration of a real annuity is longer than that of a nominal annuity, so that the insurer s cost of providing a real annuity is more sensitive to future developments in mortality patterns. Explaining the observed price dispersion in annuity markets is an important task for future research. 6

9 1.2 Evaluating the Money s Worth of Nominal and Real Annuities To evaluate the administrative and other costs associated with the individual annuities offered in the U.K. market, we compute the expected present discounted value (EPDV) of payouts for the average nominal and the average index-linked annuity. We compare this EPDV with the premium cost of the annuity to obtain a measure of the money s worth of the individual annuity. Similar measures are available for annuities offered in the United States; Warshawsky (1988) reports calculations for the period from 1920 to the early 1980s, MPWB (1999) examine data through 1995, and Poterba and Warshawsky (1998) offer results for mid The formula used to calculate the EPDV of a nominal annuity with a monthly payout A n, purchased by an individual of age b, is: (1) V b 12*(115 b) An * P j ( An ) = j=1. j Πk=1(1+ik ) We assume that no annuity buyer lives beyond age 115 and we truncate the annuity calculation after 12*(115-b) months. P j denotes the probability that an individual of age b years at the time of the annuity purchase survives for at least j months after buying the annuity. The variable i k denotes the one-month nominal interest rate k months after the annuity purchase. For a real annuity, this expression must be modified to recognize that the amount of the payout is time-varying in nominal terms but fixed in real terms. The easiest way to handle this is to allow A r to denote the real monthly payout, and to replace the nominal interest rates in the denominator of (1) with corresponding real interest rates. We use r k to denote the one-month real interest rate k months after the annuity purchase. Such real interest rates can be constructed from the UK yield curve for index-linked Treasury securities. The expression that we evaluate to compute the EPDV of a real annuity is: (2) V b 12*(115 b) Ar * P j ( Ar ) = j=1. j Πk=1(1+ rk ) We evaluate (1) and (2) using U.K. population projected survival probabilities compiled by H.M. Treasury. We use cohort mortality tables for those who reached age 60, 65, or 70 in We were not 7

10 able to obtain mortality tables corresponding to the annuitant population. By using population mortality tables, we are in effect asking what the EPDV of the average annuity would be when viewed from the perspective of an average individual in the population. Of course, the average annuity buyer and the average person in the population may be different, to the extent that annuitants have longer life expectancies. Since a real annuity offers larger payouts near the end of life than a nominal annuity does, using a population rather than an annuitant mortality table overstates the effective cost of purchasing an inflation-indexed annuity relative to a nominal annuity. Table 2 reports EPDV calculations for single life annuities for men and women of different ages in the compulsory U.K. annuity marketplace. Results for the average annuity payout are given as a simple average across the firms in our sample; we also provide the EPDV using average payouts for the three highest and three lowest annuity payout firms in our sample. The results show that the cost of buying an inflation-protected annuity in the United Kingdom is about five percent of the annuity premium. Also, the EPDV of a nominal annuity contract purchased in conjunction with a qualified retirement saving plan is five percent higher than that for a real annuity. While the EPDV for nominal annuities is approximately 90 percent of the premium cost, the analogous EPDV for real annuities averages roughly 85 percent. This difference in EPDVs might explain Diamond s (1997) claim that most annuitants in the United Kingdom elect nominal rather than real annuities. Some of the apparent cost of inflation protection may arise from adverse selection across the various types of annuities. That is, if annuitants who anticipate that they will live much longer than the average annuitant tend to purchase real annuities, then mortality rates for those who buy real annuities may be lower than those for nominal annuity buyers. Whether such mortality differences actually explain the payout differences between nominal and real annuities is not yet known. These estimates of the U.K. expected present discounted value of nominal annuity payouts are somewhat higher than our estimates of EPDV for U.S. nominal annuity products around roughly the same date. For example, in 1998, the average EPDV on U.S. nominal annuity contracts available to 65-yearold men (using the population mortality table) was 84 percent for annuities purchased through qualified 8

11 retirement saving plans (Poterba and Warshawsky, 1998). The lower U.S. payout may reflect crosscountry differences in the degree of mortality selection, relative to the population as a whole, in the qualified (U.S.) and compulsory (U.K.) annuity markets. Table 2 also suggests that there are systematic patterns in the money s worth values across age groups for both nominal and real annuities in the U.K. market. The EPDV declines as a function of the annuitant s age at the time the annuity is purchased. An explanation for this pattern may be that those who retire later tend to have lower mortality rates than those who retire earlier. Age at retirement and age at annuity purchase may be linked more closely in the market for compulsory retirement annuities than in the market for non-compulsory annuities. We suspect that many compulsory annuity buyers purchase their annuities when they retire, even though current U.K. rules do not require such purchases. The results in Table 2 also suggest that for a retiree of given age/sex characteristics there is frequently a ten percent difference between the average annuity payout for the firms offering the highest payout annuities and the firms offering the lowest payouts. Such dispersion is consistent with earlier evidence suggesting substantial pricing differences in the U.S. market for nominal annuities (MPWB, 1999). This raises the question of how potential annuitants choose among the various annuity products. In the U.S. case, there is little evidence of strong correlation between factors such as the credit rating of the insurance company offering the annuity and the EPDV paid out (MPWB, 1999). In sum, one lesson from the widespread availability of index-linked annuities the U.K. annuity market is that it is possible for private insurers to develop and offer real annuity products. This is surely easier in a nation with a well-developed market for index-linked bonds. A second lesson is that, based on nominal and real annuity pricing, the costs of obtaining inflation insurance are less than five percent of the purchase price of a nominal annuity. 2. Real Annuities in the United States: TIAA-CREF and ILONA The U.S. individual annuity market differs from that in the U.K. in that virtually all annuity products are nominal annuities. Individuals can purchase a variety of products with a graded payout 9

12 structure, so that the nominal value of their payouts (and, for low enough inflation rates, the real value of payouts) is expected to rise over time. There are only two annuity products that we are aware of that promise some degree of inflation protection. The first is the Freedom CPI Indexed Income Annuity, offered by the Irish Life Company of North America (ILONA), and the second is the Inflation Linked Bond Account annuity, offered by TIAA-CREF. In this section we describe how these products work, their current prices and payouts, and the degree to which they provide inflation protection for annuity buyers. We also note that since Treasury Inflation Protection Securities (TIPS) were introduced to the U.S. market only recently, additional insurers may offer real annuities as familiarity with these new assets grows. Insurance companies can hedge the inflation risk associated with these price level indexed annuity products by purchasing TIPS bonds. 2.1 The ILONA Real Annuity Irish Life PLC, an international insurance firm headquartered in Dublin, Ireland, offers indexlinked annuities in the United States through the Interstate Assurance Company, which is a division of Irish Life of North America (ILONA). Interstate is a well-regarded company: it had assets of $1.3 billion and it received a AA rating from Duff and Phelps, an A rating from A.M. Best and Company, and a AArating from Standard and Poors in The indexed annuity product from ILONA is the Freedom CPI Indexed Income Annuity. The annuity payout rises annually in step with the increase in the prior year s CPI. Annuity benefits from the Freedom CPI Indexed Income Annuity are guaranteed to never decline in nominal terms, even if the CPI were to fall from year to year. The minimum purchase requirement for the ILONA annuity product is $10,000, and the maximum purchase is $1 million. The annuity is available to individuals between the ages of 65 and 85. There are various payout options, including simple life annuities, annuities that provide a fixed numbers of years of payouts for certain, and refund annuities. These annuity products are available both as individual and as joint and survivor annuities. Although ILONA offers this real annuity product in the US, the agent whom we contacted indicated that thus far no sales of these annuities have been recorded. 10

13 Data were obtained on the monthly payouts offered by ILONA s indexed and nominal single premium immediate annuities for men and women age 65, 70, and 75, assuming a premium of $1 million in each case. We also obtained data on joint-and-survivor annuities with 100 percent survivor benefits. Policies purchased in mid-1998 offered a monthly payout on a real annuity at the start of the annuity contract about 30 percent smaller than the payout on a nominal annuity issued to the same individual. Table 3 shows that for men at age 65, the ratio of real to nominal payouts is 69 percent. For women at 65, the ratio is 66 percent, potentially reflecting the longer life expectancy and therefore greater back-loading that occurs with a real rather than a nominal annuity for women rather than for men. To determine the payouts relative to premium cost for these annuities, we again calculate the EPDV of annuity payouts for each of the ILONA policies quoted using a procedure similar to that described above. (Interest and mortality rates differ somewhat relative to the U.K. calculations). For discount factors in our EPDV calculations, we use the nominal yield curve for zero-coupon U.S. Treasury bonds. We start from the term structure of yields for zero-coupon Treasury strips, and work out the pattern of monthly interest rates implied by these yields under the simple expectations theory of the term structure. Data on the zero-coupon yield curve are published each Thursday in the Wall Street Journal, and we use information from the beginning of June Because we do not know the precise date at which ILONA offered the annuities we are pricing, and in light of the absence of transactions in this annuity market, we select the June 1998 term structure as an approximate guide to discount rates in mid When evaluating the EPDV of the ILONA real annuity, we use the implied short-term real interest rates that can be derived from the term structure of real interest rates of Treasury Inflation Protection Securities; once again we use these rates from early June With regard to survival patterns, we have access to two distinct mortality tables for the U.S. The first, developed by the Social Security Administration s Office of the Actuary and reported in Bell, Wade, and Goss (1992), applies to the entire population. We update this mortality table to reflect the prospective mortality rates of a 65-year old (or 70- or 75-year old) purchasing an annuity in For example, in estimating the money s worth of an annuity for a 65 year old in 1998, we use the projected mortality 11

14 experience of the 1933 birth cohort. A second set of projected mortality rates corresponds to that relevant to current annuitants. MPWB (1999) develop an algorithm that combines information from the Annuity 2000 mortality table, described in Johansen (1996), the older 1983 Individual Annuitant Mortality table, and the projected rate of mortality improvement implicit in the difference between the Social Security Administration s cohort and period mortality tables for the population. This algorithm generates projected mortality rates for the set of annuitants purchasing annuity contracts in a given year. It is worth noting that the population and annuitant mortality rates differ. For instance, the 1995 annual mortality rate for annuitants age was roughly half that for the general population (MPWB 1999). This mortality differential generates a substantially larger EPDV of annuity payouts using the annuitant versus the population mortality table. Table 4 reports EPDV calculations for Irish Life real and nominal annuities. (All EPDV calculations use pretax annuity payouts and before-tax interest rates. MPWB (1999) show that pre-tax and post-tax EPDV calculations for U.S. nominal annuities yield similar results.). For nominal annuities and using the population mortality table, the expected present discounted value of payouts for men is approximately 85 cents per premium dollar and 89 cents for women. These values are slightly higher than the average EPDV values based on nominal annuities described in A.M. Best s annuity survey of June 1998 (Poterba and Warshawsky, 1998). Using the annuitant mortality table for nominal annuities, the EPDV proves to be worth a much larger share of premium value, approximately 98 cents per dollar for men and 97 cents for women. We next turn to EPDV results for the ILONA real annuity computed using the real interest rates implicit in the TIPS yield curve, and we see that the value per dollar of premium is much lower than for the nominal annuity. For instance, a 65-year-old man purchasing a real annuity would expect an EPDV of 70 percent, versus 86 percent for the nominal annuity. At other ages a similar pattern applies: the money s worth for the real annuity products is typically percent lower than that for nominal annuities. The fact that inflation protection adds more than 15 percent to the annuity s cost may explain the limited demand for this product in the U.S. 12

15 2.2 Annuities Linked to the CREF Index-Linked Bond Account (ILBA) In May of 1997 the College Equities Retirement Fund (CREF) launched a new investment account, one that was intended to appeal to those who are saving for retirement as well as to retirees receiving annuity payouts. This product, called the CREF Inflation-Linked Bond Account (ILBA), followed from the federal government s decision to issue TIPS on January 29, TIAA-CREF indicated that its new inflation-linked account was expected to be useful for providing participants with another investment option that can enhance portfolio diversification and mitigate the long-term impact of inflation on their retirement accumulations and benefits (TIAA-CREF 1997a). The fund s goal was described as seeking a long-term rate of return that outpaces inflation, through a portfolio of inflationindexed bonds and other securities (TIAA-CREF 1997b). The CREF Inflation-Linked Bond Account has grown slowly since its inception. At the end of September 1998, the account had attracted investments of only $131 million, making it the smallest of all the retirement funds offered by TIAA-CREF. To place this amount in context, on the same date the CREF Stock fund held $96.9 billion (75 times as much as the ILBA), the TIAA Traditional Annuity fund held $94.3 billion, and all other TIAA-CREF retirement funds combined held about $25 billion. Most of the funds held in the ILBA are in the accounts of TIAA-CREF active participants, rather than retirees, and as such they are still accumulating rather than drawing down assets. To describe the inflation protection that an annuity linked to the CREF ILBA provides, we need to provide some background both on the structure of this account, on the basic structure of variable annuity products, and on the specific operation of the CREF variable annuity. The CREF Index-Linked Bond Account The ILBA invests mainly in inflation-indexed bonds issued or guaranteed by the US government, or its agencies and instrumentalities, and in other inflationindexed securities with foreign securities capped at 25% of the assets (TIAA-CREF 1998a). At present the ILBA holds 98 percent of its assets in U.S. government inflation-linked securities and 2 percent shortterm investments maturing in less than one year. In principle, the fund s asset allocation could become broader in the future, with corporate inflation-indexed securities and those issued by foreign governments 13

16 potentially being included as well as money market instruments. Expenses total 31 basis points annually which is probably explained by the small size of the fund and the fact that it is a new account. This expense ratio is lower than many mutual and pension fund expense levels, but it is as high as other, more actively managed CREF accounts such as the Stock Account (31 basis points) and the Bond Market Account (29 basis points) (see The ILBA has no sales, surrender, or premium charges. Participants may elect this account as one of several investment vehicles into which new retirement contributions may be made, and/or into which existing assets from other TIAA-CREF accounts may be transferred. As with other CREF accounts, the participant is limited to one transfer per business day in or out of the account during the accumulation phase. The ILBA may used as a vehicle for accumulating retirement assets, or it can be used to back the payment stream for a variable payout annuity. Most of our interest focuses on the second function. The ILBA account is marked to market daily, meaning that asset values fluctuate and the account could lose money. For example, if real interest rates rose due to a decline in expected inflation, bond prices could fall. As the Fund Prospectus points out, in such an event the inflation-linked bond fund s total return would then not actually track inflation every year (TIAA-CREF 1998b). This is a key feature of the ILBA, and it means that the account does not effectively offer a real payout stream to annuitants who purchase variable payout annuities tied to the ILBA. Real interest rate changes are not the only source of variation in ILBA returns. If the principal value of inflation-linked bonds changes in response to inflation shocks, perhaps because investors infer something about the future of real interest rates from inflation news, this would also affect the returns on the ILBA. Similarly, changes in the definition of the CPI might affect the ILBA return. The ILBA return for 1998 were 3.48 percent. This made it the lowest earning fund of all the taxqualified accounts offered by TIAA-CREF in 1998, as Table 5 illustrates. Daily returns on the ILBA can sometimes be negative. Variable Annuities: General Structure An annuity with payouts that rise and fall with the value of the CREF ILBA fund is a special case of a variable payout annuity. The key distinction between a fixed 14

17 annuity (including a graded fixed annuity with a pre-specified set of changing nominal payouts over time) and a variable annuity is that the payouts on a variable annuity cannot be specified for certain at the beginning of the payout period. Rather, a variable annuity is defined by an initial payout amount, which we shall denote A(0), and an updating rule that relates the annuity payout in future periods to the previous payout and the intervening returns on the portfolio that backs the variable annuity. To determine the initial nominal payout on a single-life variable annuity, per dollar of annuity purchase, the insurance company solves an equation like T A(0) * P (3) 1 = j=1 j (1 + R) j where R is the variable annuity s Assumed Interest Rate or the Annuity Valuation Rate as in Bodie and Pesando (1983). T is the maximum potential lifespan of the annuitant. This expression would require modification if there were a guarantee of some number of certain payments or some other additional structure imposed on the annuity payouts. This expression ignores expenses and other administrative costs associated with the sales of annuities or the operation of insurance companies. The annuity updating rule depends on the return on the assets that back the annuity, which we denote by z t, according to: (4) A(t+1) = A(t)*(1+z t )/(1+R). The frequency at which payouts are updated varies across annuity products, and there is no requirement that the payout be updated every time it is paid. (Thus, one might have an annuity with monthly payouts but quarterly updating.) In designing a variable annuity, the assumed interest rate (R) is a key parameter. Assuming a high value of R will enable the insurance company to offer a large initial premium, but, for any underlying portfolio, the stream of future payouts will be more likely to decline as the assumed value of R rises. Equation (4) clearly indicates that an individual who purchases a variable annuity will receive payouts that fluctuate with the nominal value of the underlying portfolio. 15

18 Specific Provisions of the CREF ILBA-Backed Annuity. When a TIAA-CREF participant terminates employment, he or she can begin receiving retirement benefits. The participant then decides how to manage the payouts from accumulated retirement accounts. This includes deciding whether to annuitize the retirement assets, how much to annuitize, and whether to use an inflation-linked annuity, subject to the proviso that individual employers may restrict retirees options. Benefits are payable monthly, though recipients may elect quarterly, semi-annual, and annual payouts as an alternative (TIAA- CREF 1998d). In addition, the participant can chose the form and duration of the payout pattern, subject to minimum distribution rules set by the IRS. If the participant chooses to annuitize part of his or her accumulation, there are a variety of potential annuity structures, including life annuities, 10- and 20-year certain payout annuities, and joint and survivor as well as single life products. Under TIAA-CREF rules, a CREF participant electing an annuity must be no older than age 90 when he or she initially applies for the annuity. The applicant must select at least one of the annuity accounts initially for the drawdown phase, and thereafter, he or she may switch from one annuity account into another as often as once per quarter (TIAA-CREF 1998a). There are restrictions on shifting funds from TIAA to CREF: this must take place over a longer horizon. While the choice of annuity fund can be altered, the form of benefit payout cannot be changed once the annuity has been issued. In order to understand how CREF annuity payments are determined, it is necessary to define the basic annuity unit value. This is an amount set each March 31 by dividing an account s total funds in payment status by the actuarial present value of the future annuity benefits to be paid out, assuming a 4 percent nominal interest rate and mortality patterns characteristics of existing CREF annuitants. A unisex version of the mortality table for individual annuitants is used when the applicant first files for an annuity set back for each complete year elapsed since 1986 (TIAA-CREF (1998d)). The same mortality table is applied to all TIAA-CREF annuity accounts, based on participant mortality experience. Mortality experience is adjusted every quarter. A newly retired participant seeking to annuitize his retirement sum must have his own accumulation amount translated into an initial annuity amount (A(0)), determined by dividing his 16

19 accumulation by the product of an annuity factor and the basic annuity unit value just described. The annuity factor reflects assumed survival probabilities based on the annuitant s age and an assumed effective Annual Interest Rate (AIR) of 4 percent nominal (TIAA-CREF 1998c). The participant s initial annuity amount is then adjusted over the life of the annuity contract on either a monthly or an annual basis, depending on the participant s election. The adjustment will reflect the actual fund earnings on a total return basis, relative to the assumed 4 percent AIR. Actual investment performance is used to update the annuity values as of May 1 for those electing to have their income change annually, or monthly for those electing monthly income changes. Because the investment returns on the underlying accounts affect annuity payouts, these TIAA-CREF annuities are variable payout annuities. The Extent of Inflation Protection. It is evident that a variable payout annuity linked to the CREF-ILBA does not provide a guaranteed inflation product, since it is marked to market daily. Thus if the price drops, or if the unit value failed to rise with inflation, the participant s unit value would not be constant in real terms. More importantly, the CREF annuity may fail to keep up with inflation because of the way in which it is designed. When the first-year annuity payout is set, it assumes the 4 percent AIR mentioned above, which is the same rate used for other CREF annuities. In subsequent years, if the unit value of the account were to rise less than 4 percent, payouts would be reduced to reflect this lower valuation. For example, the total return (after expenses) on the ILBA account for 1998 was 3.48 percent. Since the AIR for the CREF annuity is 4 percent, an annuity in its second or later year payout phase would experience a decline in payout of 0.52 percent. This adjustment to future payout levels does not necessarily correspond to the CPI inflation rate in In our example, if the annual inflation rate for 1998 were anything greater than one percent, the real value of annuity payouts for those holding ILBA-backed variable annuities would decline in 1999 and subsequent years. The only way a second or subsequent-year payout could be guaranteed not to decline in real terms would be if the real return on the account, i.e. on Treasury Inflation Protection Securities, always exceeded 4 percent. It does not at present. 17

20 The precise extent to which payouts on ILBA-backed variable annuities will vary in real terms in the future is an open question. If the prices of inflation-linked bonds are bid up during high-inflation periods, and real interest rates decline at such times, this will partly protect the ILBA account value. One relevant comparison for potential annuitants, however, may be between holding a CREF ILBA-backed variable annuity, and purchasing TIPS bonds directly. Two considerations are relevant to such a comparison. First, the TIPS bonds offer a more direct form of inflation protection, although they do not provide any risk-sharing with respect to mortality risk. Second, there are tax differences between the two investment strategies. TIPS would be taxable if they were not held in a qualified pension account, while the income from bonds held in the CREF ILBA-backed account is not taxed until the proceeds are withdrawn. The CREF variable payout annuity linked to the ILBA would be more likely to deliver a future real payout stream if the AIR on this annuity were set equal to the real interest rate on long-term TIPS at the time when the annuity is purchased. In this case, the return on the bond portfolio would typically equal the AIR plus the annual inflation rate, leaving aside some of the risks of holding indexed bonds such as changes in the way the CPI is constructed. This would provide a mechanism for delivering something closer to a real annuity payout stream. One difficulty with this approach is that it would make it more difficult for annuitants to take advantage of some of the investment flexibilities currently provided by CREF. At present, all CREF annuities assume the same AIR, regardless of the assets that back them. This facilitates conversions from one annuity type to another. To date, there has been very limited demand for CREF s ILBA-backed variable payout annuities. This lack of demand raises the perennial question of why retirees are not more concerned about inflation protection. One reason often given is inflation illusion ; that is, people simply do not understand how inflation erodes purchasing power. Another reason may be that inflation-proof assets are new so that investors have not yet learned how to think about such assets. Hammond (1998) notes that inflationlinked bonds in other countries took some time to become popular after they were introduced: After a flurry of initial interest, inflation bonds in those countries went through a period of quiescence -- low 18

21 liquidity and little interest. Then, with some sort of trigger renewed inflation or a strong commitment on the part of central government the market picked up and people began to figure out what the bonds were good for. In the U.K. this process took about ten years. The United States today may be in the early stages of this process. 2.3 Conclusions About Real Annuities in the United States Our analysis of the ILONA and TIAA-CREF experience suggests that there is currently no market for genuine real annuities in the United States. While ILONA offers a product that guarantees a real stream of payouts, no one has yet purchased this annuity. This may reflect the fact that the instrument s pricing requires relatively high rates of inflation to generate benefits with expected present discounted values similar to those of nominal annuities offered by ILONA and other insurers. The inflation-linked bond account offered by CREF has attracted investment funds since it became available in 1997, but the CREF variable annuities with payouts linked to returns on inflation indexed bonds does not guarantee its buyers a constant real payout stream. Although in practice it may come close to delivering a constant real payout, its performance will depend on the as yet uncertain price movements in the prices of Treasury Inflation Protecton Securities. 3. Asset Returns and Inflation: Another Route to Inflation Insurance The last two sections focused on insurance contracts that explicitly provide a constant real income stream for retirees. In this section we consider the possibility of using variable payout annuities linked to assets other than indexed bonds as an alternative means of avoiding inflation risk. Such variable payout annuities can reduce the impact of inflation in two ways. First, they may offer higher average returns than the assets that are used in pricing real and nominal annuities. These returns may, of course, come at the price of greater payout variability. Second, it is possible that the returns on the assets that underlie the variable payout annuities may move in tandem with inflation. In this case a variable payout annuity could provide a form of inflation insurance. 19

22 To examine these arguments, we begin by summarizing the well-known historical real return performance of U.S. stocks, bonds, and Treasury bill investments. We do this by considering an individual who considers investing one dollar in cash, or in a portfolio of Treasury bills, long-term bonds, or corporate stock. We calculate the real value of an initial $1 investment after 5, 10, 20, and 30 years. We first perform this calculation in 1926, so that the 30-year return interval concludes in We then repeat the calculation in 1927, 1928, and all subsequent years in which we have enough data to calculate long-term returns. The last year for which we have return information is 1997, so we finish our five year calculations in 1993, our ten year calculations in 1988, and so on. To summarize the results on the real value of each investment, we calculate both the average real value of each investment, averaged across all of the years with sufficient data. We also compute the standard deviation of this real return. The results of these calculations appear in Table 6. The underlying calculations have been done using actual returns on stocks, bills and, bonds over the period. For the return after five (30) years, there are 66 (41) overlapping return intervals. The results in Table 6 show that holding cash worth $1 initially would have an average real value of only 49 cents after 20 years on average. In contrast, a $1 initial investment in bills or bonds would have increased in real value. For bills, the cumulative real return over 20 years was 1.3 percent, while for bonds, it was 16.1 percent. The last column of Table 6 shows comparable calculations for corporate stock. Here the real value of the investment after 20 years would have increased by a factor of 4.5. This implies that an investor who purchased an income stream tied to the total return on the U.S. stock market, such as an equity-linked variable annuity, would have the potential to receive a higher real income stream late in retirement than at the beginning of retirement. This stands in stark contrast to the declining real value of the payouts on a fixed nominal stream, such as a nominal annuity contract. The substantial real return on U.S. equities suggests that one method of obtaining partial longterm protection against inflationary erosion of annuity payouts might be to purchase a portfolio of equities, and then to link annuity payouts to equity returns. In practice, however, variable annuity policies that offer payouts linked to equity returns do not guarantee real payouts that rise as steeply as Table 6 20

23 suggests. This is because the payouts on a variable annuity depend on the performance of the underlying assets relative to the Assumed Interest Rate (AIR) on the annuity product (R in equation (3)) as Bodie and Pesando (1983) explain in detail. Therefore the variable annuity payout for an equity-linked variable annuity can only rise over time if the equity portfolio returns more than the assumed value of R used in designing the annuity. Bodie and Pesando (1983) assume that R equals the historical average return on the assets that back the annuity, but in practice we have found that nominal R values of 3 or 4 percent per year are common in the current variable payout annuity market. This is true even for equity-backed annuities. One should note that if a variable payout annuity assumed R = 0, then the real payouts in Table 6 would in fact describe the experience of an annuitant, since the nominal payout recursion would become A(t+1) = A(t)*(1+z t ). The high average real return on equities implies that an investor holding U.S. stocks over the last seven decades would have experienced a rising real wealth profile. But to study whether this is because equities provide a good inflation hedge, we must explore the way U.S. equity returns covary with shocks to the inflation rate. If stocks generate positive returns when the inflation rate rises unexpectedly, then equities operate as an inflation hedge. The fact that U.S. equities have generated substantial positive returns over the period since 1926 does not provide any information on the correlation between inflation and stock returns. We investigate the historical covariances between real U.S. stock returns, bond returns, and bill returns, and unexpected inflation shocks, over the , and , periods. If the real return on a particular asset category is not affected by unexpected inflation, then that asset can serve as a valuable inflation hedge. If the real return on the asset declines when inflation rises unexpectedly, however, then that asset does not provide an inflation hedge. The first step in our analysis involves estimating of a time series for unexpected inflation. We do this by estimating fourth-order autoregessive models relating annual inflation (π t ) to its own lagged values, or to its own lagged values as well as those of nominal Treasury bill rates (i t ). The basic regression specification is either 21